It supposedly doesn't monitor the contents of your pages, but it knows just about everything else.
In addition to tracking the printer’s online or offline status, page count, and ink levels, your rented printer will look at the types of documents you’re printing (e.g., PDF, JPG, Word), the types of devices that initiated the print job, “peripheral devices,” and other “metrics” related to the service, the All-In Plan’s terms read. This is on top of the personal information HP collects upon initiating the plan, like your location and your company name (if you have one). By signing up for the service, the terms say, you “grant to HP a non-exclusive, worldwide, royalty-free right to use, copy, store, transmit, modify, create derivative works of and display [your] non-personal data for its business purposes.”
Unless you are a business getting printers on commercial leases, do yourself a favour and just buy a Brother laser printer and stop having issues with printers and start saving money as well.